Decomposition of closed orientable geometric surfaces into acute geodesic triangles

Abstract

We prove that for every \(g\ge 2\), a differentiable closed orientable geometric surface of genus g may be decomposed into \(16g-16\) acute geodesic triangles. We also determine the number of acute geodesic triangles needed for the sphere and the torus.

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Corresponding author

Correspondence to Stephen M. Gagola III.

Additional information

The work of this paper was supported by NRF Competitive Grant No.: CPRR/93507, 2015.

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Bau, S., Gagola, S.M. Decomposition of closed orientable geometric surfaces into acute geodesic triangles. Arch. Math. 110, 81–89 (2018). https://doi.org/10.1007/s00013-017-1097-1

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Keywords

  • Acute
  • Decomposition
  • Geodesic
  • Orientable
  • Surface
  • Triangle

Mathematics Subject Classification

  • 53A05
  • 51H25